In the Bohr's model of hy drogen atom, the electron moves around the nucleus in a circular orbit of radius `5xx10^(-11) m`. Its time period is `1.5xx10^(-16)s`. The current associated with the electron motion is:-

Options

A. zero
B. `1.6xx10^(-19)A`
C. `0.17A`
D. `1.07xx10^(-3)A`

Explanation

To find the current associated with the electron motion in the Bohr model of the hydrogen atom, we can use the following steps:

### Step 1: Understand the Concept of Current
Current (I) is defined as the charge (Q) passing through a point in a circuit per unit time (t). Mathematically, it is expressed as:
\[ I = \frac{Q}{t} \]

### Step 2: Identify the Charge of the Electron
The charge of an electron (Q) is approximately:
\[ Q = -1.6 \times 10^{-19} \, \text{C} \]
(Note: The negative sign indicates the charge is negative, but for current calculation, we consider the magnitude.)

### Step 3: Use the Given Time Period
The time period (T) of the electron's motion is given as:
\[ T = 1.5 \times 10^{-16} \, \text{s} \]

### Step 4: Calculate the Current
Using the formula for current, we substitute the values of charge and time period:
\[ I = \frac{Q}{T} = \frac{1.6 \times 10^{-19} \, \text{C}}{1.5 \times 10^{-16} \, \text{s}} \]

### Step 5: Perform the Calculation
Now, we can calculate the current:
\[ I = \frac{1.6 \times 10^{-19}}{1.5 \times 10^{-16}} \]
\[ I = \frac{1.6}{1.5} \times 10^{-3} \]
\[ I \approx 1.067 \times 10^{-3} \, \text{A} \]

### Final Answer
The current associated with the electron motion is approximately:
\[ I \approx 1.067 \, \text{mA} \]

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